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"Normal vector" redirects here. For "normalized vector" (a vector of length one), see unit vector. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. A normal to a non-flat surface at a point p on the surface is a vector which is perpendicular to the tangent plane to that surface at p. The word normal is also used as an adjective as well as a noun with this meaning: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalises to orthogonality.
Calculating a surface normal For a polygon (such as a triangle), a surface normal can be calculated as the vector cross product of two (non-parallel) edges of the polygon. For a plane given by the equation , the vector is a normal. If a (possibly non-flat) surface S is parametrized by a system of curvilinear coordinates x(s, t), with s and t real variables, then a normal is given by the cross product of the partial derivatives If a surface S is given implicitly, as the set of points satisfying , then, a normal at a point on the surface is given by the gradient abla F(x, y, z). If a surface does not have a tangent plane at a point, it does not have a normal at that point either. For example, a cone does not have a normal at its tip nor does it have a normal along the edge of its base. However, the normal to the cone is defined almost everywhere. In general, it is possible to define a normal almost everywhere for a surface that is Lipschitz continuous. Uniqueness of the normal A normal to a surface does not have a unique direction; the vector pointing in the opposite direction of a surface normal is also a surface normal. For an oriented surface, the surface normal is usually determined by the right-hand rule. Uses | ||||||||
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